Cremona's table of elliptic curves

15312 = 2⁴ · 3 · 11 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 29+	Signs for the Atkin-Lehner involutions
Class	15312q	Isogeny class
Conductor	15312	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-67958107635449856 = -1 · 219 · 3 · 116 · 293	Discriminant
Eigenvalues	2- 3+ -3  1 11- -4  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-568752,165759936]	[a1,a2,a3,a4,a6]
Generators	[200:7744:1]	Generators of the group modulo torsion
j	-4967448100211756593/16591334871936	j-invariant
L	3.1987304308045	L(r)(E,1)/r!
Ω	0.34888841607279	Real period
R	0.38201450227871	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1914n2 61248ce2 45936bo2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 15312q2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-3	1	-	-4	3	1	6	+	-2	-7	-9	7	9	-6	-15	2	-14	12	14	10	12	-6	14

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Quadratic twists for elliptic curve 15312q2

-4	8	-3
1914n2	61248ce2	45936bo2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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